Q. 59 - Calculus

Question

Use integration formulas to solve each integral in Exercises 21–62. You may have to use algebra, educated guess- and- check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating. (Hint for Exercise 54: $\tan \left(x\right) = \frac{\sin \left(x\right)}{\cos \left(x\right)}$).

$\int 3\cos h \left(2x\right)dx.$

Step-by-Step Solution

Answer

The value of the integral is $\frac{3}{2}\sin h \left(2x\right) +c$

Step 1. Given Information.

Given is a integral: $\int 3\cos h \left(2x\right)dx.$

Step 2. Formula involved.

$\int \cos h x dx = \sin h x +c$.

Step 3. Solving the integral.

$$\begin{gathered} \int 3\cos h \left(2x\right)dx \\ Let t = 2x \\ dt = 2dx \\ = 3\int \cos h \left(t\right) \frac{dt}{2} \\ =\frac{3}{2} \sin h \left(t\right) +c = \frac{3}{2}\sin h \left(2x\right) +c. \end{gathered}$$